The MA originates from spin-orbit coupling and is here defined as the energy difference between in-plane and out-of-plane orientation of the magnetic moments, see Eq. (REF ). With our definition, a negative MA corresponds to an out-of-plane easy axis. We note that most of the materials in the C2DB are nearly isotropic in-plane. Consequently, if the easy axis lies in the plane, the spins will exhibit an approximate in-plane rotational symmetry, which prohibits magnetic order at finite temperatures. Since spin-orbit coupling becomes large for heavy elements, we generally expect to find larger MA for materials containing heavier elements. In general the magnitude of the MA is small. For example, for monolayer CrI\(_3\)  with a Curie temperature of 45 K[1]} we find a MA of \(-0.85\)  meV per Cr atom in agreement with previous calculations[2]}. Although small, the MA is, however, crucial for magnetic order to emerge at finite temperature.
